A one-dimensional, continuous, regular, and strong Markov process $X$ with state space $E$ hits any point $z \in E$ fast with positive probability. To wit, if $\tau_z = \inf \{t \geq 0:X_{t} = z\}$, then $P_\xi({ \tau}_z 0$ for all $\xi \in E$ and $\varepsilon>0$.
Topics: Mathematics, Probability
Source: http://arxiv.org/abs/1508.03822
This article is from Diabetes , volume 61 . Abstract : Interest in how the gut microbiome can influence the metabolic state of the host has recently heightened. One postulated link is bacterial fermentation of “indigestible” prebiotics to short-chain fatty acids (SCFAs), which in turn modulate the release of gut hormones controlling insulin release and appetite. We show here that SCFAs trigger secretion of the incretin hormone glucagon-like peptide (GLP)-1 from mixed colonic cultures in...
Source: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3266401